1. Field of the Invention
The invention relates to the use of operator group properties of the fractional Fourier transform for correction of mis-focus in stored digital images produced by coherent optics such as laser imaging, transmission electron microscope imaging, particle-beam imaging, coherent X-ray imaging, etc. More specifically, the invention relates to the creation of centered discrete fractional Fourier transformations with high-accuracy orthonormal eigenvectors for the correction of underfocus and overfocus, and for an automatic control system that automatically improves the focus of a mis-focused image.
2. Background of the Invention
Although consumer cameras increasingly provide automatic focusing features useful at the time of shooting, in many situations all that exists is an image or video that is out-of-focus and the scene or situation cannot be repeated for the benefit of a new photograph or video to be taken.
The term “blur” is usually reserved for motion blur rather than mis-focus effects, although the term “blur” can include mis-focus effects. However, mis-focus (resulting from misadjusted optics, such as a lens mis-setting) fundamentally differs from motion blur (resulting from motion of the subject or the camera).
Motion blur is relatively easily corrected with numerous textbook algorithms [4,5] and several available current products. Numerous techniques have been developed for the correction of motion blur. However, mis-focus effects are fundamentally different from motion blur. Statistically-based processes useful for motion blur can be applied the effects of mis-focus, and can in some cases offer marginal improvement, but a corrected focus is outside the reach of such algorithms. Typically attempts to correct mis-focus with blur correction or any other known techniques almost without fail give very poor results. Aside from the body of work to which this patent application pertains, there are no known mis-focus correction algorithms, Thus if one has a photograph or video of an irreproducible situation that is out-of-focus, there has been simply no recourse.
Image mis-focus is not restricted to conventional optical systems such as photography, video, and optical microscopes. Image mis-focus also occurs with laser systems, electron microscope imaging, particle-beam imaging, coherent X-ray imaging, etc. This second collection of applications employs coherent electromagnetic radiation. In contrast, conventional optical systems such as film and digital photography, video cameras, and optical microscopes employ normal light (“incoherent electromagnetic radiation”).
This invention addresses the need for correcting mis-focus in existing images created by “coherent electromagnetic radiation” imaging. The technique includes use of a mathematical transformation known as a fractional Fourier transform [1-3]. The invention uses algorithms executing on a processor to numerically correct underfocus and/or overfocus conditions in images or portions of images created with coherent light (laser), coherent electron beams (transmission electron microscopes), and potentially those of coherent microwaves (masers), coherent X-ray imaging, and other coherent imaging systems.
In an example realization, the invention corrects mis-focus of at least a portion of an image created from coherent imaging in an image file on a numerical processor using a two-dimensional centered fractional Fourier transform or mathematical equivalents. A received image is presented to a numerical processor, and a first numerical value for a variable α is selected and used in an iterative algorithm executing on the numerical processor. A two-dimensional centered discrete fractional Fourier transform operator of power α and a phase correction operator associated with a two-dimensional centered discrete fractional Fourier transform matrix of power 2-α are both applied to the at least a portion of the image file to produce a modified at least a portion of the image file which is inspected. A change in the mis-focused condition with respect to the original mis-focused condition is determined and used in adjusting the numerical value for the variable α to a new value for use in a next iteration of the numerical procedure. If real values for α between 0 and a real number β do not result in a desired outcome, α is adjusted to a complex value of the form β+χ where χ is an imaginary number.